Book 4
5
Again, there will also be an intermediate in all classes in which the negation of a term implies the contrary assertion; e.g., among numbers there will be a number which is neither odd nor not-odd. But this is impossible, as is clear from the definition.What definition Aristotle had in mind we cannot tell; but it must have stated that every number is either even or odd.
5
Again, there will be an infinite progression, and existing things will be not only half as many again, but even more.
6
For again it will be possible to deny the intermediate in reference both to its assertion and to its negation, and the result will be somethingIf besides A and not-A there is an intermediate B, besides B and not-B there will be an intermediate C which is neither B nor not-B; and so on.; for its essence is something distinct.
6
Again, when a man is asked whether a thing is white and says no, he has denied nothing except that it is 〈white〉, and its not-being 〈white〉 is a negation.
7
Now this view has occurred to certain people in just the same way as other paradoxes have also occurred; for when they cannot find a way out from eristic arguments, they submit to the argument and admit that the conclusion is true. Some, then, hold the theory for this kind of reason, and others because they require an explanation for everything. In dealing with all such persons the starting-point is from definition;
